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INdAM Fellowship Programs in Mathematics and/or Applications cofunded by Marie Skłodowska-Curie Actions



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Maria Infusino

INdAM-COFUND Outgoing fellow between 2012-11-05 and 2014-11-04

Project information

Title

RQRP: Realizability and Quantum Representability Problem

Outgoing host organisation                                              Return host organisation

University of Reading                                                                    Università  degli Studi di Roma “La Sapienza”

Whiteknigths House                                                                      Piazzale Aldo Moro, 5
PO BOX 217                                                                                     00185 Roma, Italy
Reading RG66AH
United Kingdom

http://www.reading.ac.uk/                                                           http://www.uniroma1.it/

Abstract

Complex systems, such as many-body systems like liquid composed of molecules, are generally very difficult to describe. The investigation of such systems is greatly facilitated if the attention is restricted to selected physical parameters (usually correlation functions) which encode the relevant structure of the system. The realizability and the quantum representability problems exactly address the question of identifying conditions to determine whether a putative characteristic can be actually realized by a state of the underlying system.

Realizability and representability arise repeatedly in different areas, thus they are promising viewpoints on complex systems. Recently, there has been a revival of interest in these problems in statistical mechanics as well as in quantum\ chemistry but progress is hindered by a lack of understanding of their mathematical structure.

The primary aim of this project is to establish rigorous mathematical foundations for the analysis of large complex systems. The innovative strategy proposed is to tackle the realizability problem from the point of view of moment theory. In fact, the finite dimensional projections of the realizability problem give a range of truncated moment problems of increasing dimension. This new approach is thought to shed some light on the problem to identify further relevant explicit conditions for realizability out of the rather inexplicit ones known in literature.

The representability problem is essentially a quantum version of the realizability problem. The methods developed in this project for the realizability problem can be, therefore, used to derive an explicit solution of the quantum representability for low densities.

Fellow information

Research interests

Measure theory, probability, number theory,
mathematical physics and functional analysis.

In particular:

  • Realizability of correlation functions and quantum representability problem.
  • Truncated moment problem and its applications.
  • Uniform distribution theory.
  • Random sequences of Steiner symmetrizations.

Previous positions, awards

  • 2011-2012: Postdoctoral Research fellow, Department
    of Mathematics, University of Reading, UK
    Research project: Truncated
    moment problems in Statistical Physics and Quantum Chemistry.

    Principal investigator: Dr Tobias Kuna.
  • February 2011: PhD in Mathematics and Computer Science
    at University of Calabria, Italy.
    Thesis title: Uniform
    distribution of sequences of points and partitions.

    Supervisor: Prof. Aljosa Volcic.
  • October 2007: MSc in Mathematics cum Laude at University of Calabria, Italy.
    Thesis title: Uniformly distributed sequences on fractal sets
    Supervisor: Prof. Aljosa Volcic.
  • October 2005: BSc in Mathematics cum Laude at University of Calabria, Italy.
    Thesis title: Newton-Kantorovich method for non-lin ear operators in
    Banach space

    Supervisor: Prof. Espedito De Pascale.
  • July 2012: Prize for The best research poster at
    the 6th European Congress of Mathematics (6ECM), Jagiellonian
    University, Kraków, Poland.
  • July 2008: Awarded The best graduate in
    2007
    from the School of Mathematics, Physics and Natural Sciences
    of University of Calabria, Italy.
  • 2002-2007: Fellowship from Fondazione
    Calabria Scienze Oggi
    . (Academic regional association which
    supports outstanding students, providing them with a more advanced
    quality education and training.)

Publications, preprints, other works

  1. M. Infusino and A. Volcic, Uniform distribution on fractals, Uniform Distribution Theory, 4 (no.2): 47-58, 2009
  2. M. Drmota and M. Infusino, On the discrepancy of some generalized Kakutani’s sequences of partitions, Uniform Distribution Theory, 7 (no.1): 75–104, 2012
  3. M. Infusino, T. Kuna, and A. Rota, Concrete conditions for realizability of moment measures via quadratic modules, in preparation
  4. M. Infusino, T. Kuna, J. L. Lebowitz, and E. R. Speer, Truncated moment problem as a special case of realizability, in preparation

Conferences, schools, other events

  • Polynomial Optimisation: Summer School and Workshop
    Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 15-19 July 2013
  • Stochastic and Infinite Dimensional Analysis
    ZIF, University of Bielefeld, Germany, 24-28 June 2013
  • Young women in discrete mathematics
    Bonn, Germany, 7-9 June 2013
  • Research visit
    Rutgers University, USA, 26 March – 26 April 2013
  • Analysis day
    University of Reading, UK, 19 October 2012
  • 6th European Congress of Mathematics
    Jagiellonian University, Poland, 1-8 July 2012
  • 107th Statistical Mechanics Conference
    Rutgers University, USA, 8 May 2012
  • XIX Conference of Italian Mathematical Society (UMI)
    University of Bologna, Italy, 12-17 September 2011
  • Spring School in Discrete Probability, Ergodic Theory and Combinatorics
    TU-Graz, Austria, 4-15 April 2011
  • II International Conference on Uniform Distribution Theory
    Strobl, Austria, 5-9 July 2010


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